To calculate Dimensional Formula of Area, we need to know its formula
Area = Length x Breadth
Area = L x L
Area = L2
So Dimensional Formula = [M0 L2 T0]
SI unit of Area is m2
Dimensional Formula is a standardized method to express the Physical quantities in terms of basic quantities as chosen in the SI system of measurement. These are denoted with symbols in square brackets []
The seven standards as per SI are
1) Mass
2) Length
3) Time
4) Electric Current [A]
5) Thermodynamical Temperature [K]
6) Luminous Intensity [Cd]
7) Amount of Substance [mol]
Area of Square (A)
Area of Square refers to the number of square units required to fill the square is called the area of square. Area is a derived physical quantity. A square metre is the area of a square whose each sides are 1 metre.
Area of the square = side × side
So,
Area of the square = L × L=L2
Hence, Dimensional formula for Area of Square =M0L2T0
The fundamentals of physics form the basis for the study and the development of engineering and technology. Measurement consists of the comparison of an unknown quantity with a known fixed quantity. The quantity used as the standard of measurement is called ‘unit’.
Fundamental physical quantities–
Fundamental quantities are the quantities which cannot be expressed in terms of any other physical quantity.
Example– length, mass and time.
Derived quantities–
A derived quantity is a quantity that is based on the result of a systematic equation that includes any of the seven basic quantities, which are the kilogram, meter, second, ampere, kelvin, mole and candela.
Examples–Area (Square meter; M2), speed (meters per second; m/s) and Density (kg/m3).
Unit –
Unit is the reference used as the standard measurement of a physical quantity. The unit in which the fundamental quantities are measured are called fundamental unit and the units used to measure derived quantities are called derived units.
System of unit –
Group of units of all physical quantities are system of unit.
There are seven fundamental units (base units) and two supplementary units.
| Quantity | Definition | Unit | Symbol |
| Fundamental quantities | |||
| Length | The longest extent of anything as measured from end to end. | Metre | M |
| Mass | A fundamental measure of the amount of matter in the object | Kilogram | Kg |
| Time | Time is the dimension on which the evolution of state of a system is allowed to occur. | Seconds | S |
| Electric current | Electric current is defined as the rate at which charge flows through a surface. | Ampere | A |
| Temperature | A measure of the warmth or coldness of an object or substance with reference to some standard value. | Kelvin | K |
| Luminous intensity | Luminous intensity is an expression of the amount of light power emanating from a point source within a solid angle of one steradian. | Candela | Cd |
| Amount of substance | Amount of substance, also called material quantity, is a dimensionless expression of the number of particles in a sample. | Mole | Mol |
| Supplementary quantities | |||
| Plane angle | Plane angle is angle between two line meeting at the vertex. | Radian | rad |
| Solid angle | Solid angle is the angle subtended by the object in three dimensional space from a point. | Steradian | sr |
| Wavelength | Solid angle is the angle subtended by the object in three dimensional space from a point. | Angstrom | A0 = 10-8 cm |